A275461 G.f.: 3F2([2/9, 5/9, 7/9], [2/3, 1], 729 x).

1, 105, 38808, 18595500, 10000998000, 5742915942960, 3440119256028000, 2122455291847675200, 1338358017590361495000, 858192528139829777895000, 557657055926757140695941600, 366299456771890110076863664500, 242765837117133913048941576656100, 162109136966873437562041203714292500

Offset

0,2

Comments

"Other hypergeometric 'blind spots' for Christol’s conjecture" - (see Bostan link).

Links

Gheorghe Coserea, Table of n, a(n) for n = 0..300

A. Bostan, S. Boukraa, G. Christol, S. Hassani, J-M. Maillard Ising n-fold integrals as diagonals of rational functions and integrality of series expansions: integrality versus modularity, arXiv:1211.6031 [math-ph], 2012.

Formula

G.f.: hypergeom([2/9, 5/9, 7/9], [2/3, 1], 729*x).

D-finite with recurrence n^2*(3*n-1)*a(n) -3*(9*n-7)*(9*n-4)*(9*n-2)*a(n-1)=0. - R. J. Mathar, Jul 27 2022

a(n) ~ (1 + 2*cos(2*Pi/9)) * Gamma(4/9) * 3^(6*n - 1/2) / (2*Pi * Gamma(1/3) * n^(10/9)). - Vaclav Kotesovec, Apr 27 2024

Example

1 + 105*x + 38808*x^2 + 18595500*x^3 + ...

Mathematica

HypergeometricPFQ[{2/9, 5/9, 7/9}, {2/3, 1}, 729 x] + O[x]^14 // CoefficientList[#, x]& (* Jean-François Alcover, Oct 23 2018 *)

Prog

(PARI) \\ system("wget http://www.jjj.de/pari/hypergeom.gpi");
read("hypergeom.gpi");
N = 12; x = 'x + O('x^N);
Vec(hypergeom([2/9, 5/9, 7/9], [2/3, 1], 729*x, N))

Crossrefs

Cf. A268545-A268555, A275051-A275054.

Sequence in context: A339847 A145621 A167779 * A054862 A348794 A028917

Adjacent sequences: A275458 A275459 A275460 * A275462 A275463 A275464

Keyword

nonn

Author

Gheorghe Coserea, Jul 31 2016

Status

approved